Presbyopia correction through negative spherical aberration

ABSTRACT

Devices, systems, and methods for treating and/or determining appropriate prescriptions for one or both eyes of a patient are particularly well-suited for addressing presbyopia, often in combination with concurrent treatments of other vision defects. High-order spherical aberration may be imposed in one or both of a patient&#39;s eyes, often as a controlled amount of negative spherical aberration extending across a pupil. A desired presbyopia-mitigating quantity of high-order spherical aberration may be defined by one or more spherical Zernike coefficients, which may be combined with Zernike coefficients generated from a wavefront aberrometer. The resulting prescription can be imposed using refractive surgical techniques such as laser eye surgery, using intraocular lenses and other implanted structures, using contact lenses, using temporary or permanent corneal reshaping techniques, and/or the like.

CROSS REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.12/436,743 filed May 6, 2009, which is a continuation of U.S. patentapplication Ser. No. 12/207,444 filed Sep. 9, 2008, now U.S. Pat. No.8,142,499 issued Mar. 27, 2012, which is a continuation of Ser. No.11/780,147 filed Jul. 19, 2007, now U.S. Pat. No. 7,478,907 issued Jan.20, 2009, which is a continuation of U.S. patent application Ser. No.11/173,904 filed Jun. 30, 2005, now U.S. Pat. No. 7,261,412 issued Aug.28, 2007, the disclosures of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

This invention relates to optical correction, and in particular providesmethods, devices, and systems for treating presbyopia and other visionconditions, for developing prescriptions for treatment of presbyopia andother vision conditions, and/or the like.

Presbyopia is a condition that affects the accommodation properties ofthe eye. As objects move closer to a young, properly functioning eye,ciliary muscle contraction and zonular relaxation may allow the lens ofthe eye to become rounder or more convex, and thus increase its opticalpower and ability to focus at near distances. Accommodation can allowthe eye to focus and refocus between near and far objects.

Presbyopia normally develops as a person ages, and is associated with anatural progressive loss of accommodation. The presbyopic eye can losethe ability to rapidly and easily refocus on objects at varyingdistances. There may also be a loss in the ability to focus on objectsat near distances. Although the condition progresses over the lifetimeof an individual, the effects of presbyopia usually become noticeableafter the age of 45 years. By the age of 65 years, the crystalline lenshas often lost almost all elastic properties and has only limitedability to change shape.

To address the vision problems associated with presbyopia, readingglasses have traditionally been used by individuals to thus allow theeye to focus on near objects and maintain a clear image. This approachis similar to that of treating hyperopia, or farsightedness.

Presbyopia has also been treated with a number of alternativeapproaches. Many presbyopes are prescribed bi-focal eyeglasses, whereone portion of the lens is corrected for distance vision and anotherportion of the lens is corrected for near vision. When peering downthrough the bifocals, the individual looks through the portion of thelens corrected for near vision. When viewing distant objects, theindividual looks higher, through the portion of the bi-focals correctedfor distance vision. Contact lenses and intra-ocular lenses (IOLs) havealso been used to treat presbyopia, for example, by relying onmonovision (where one eye is corrected for distance-vision, while theother eye is corrected for near-vision) or bilateral correction witheither bi-focal or multi-focal lenses. In the field of refractivesurgery, ablation profiles have been suggested to treat presbyopia,often with the goal of passively increasing the range of focus of theeye.

While the known and proposed methods for treatment of presbyopia havehad varying degrees of success, none has proven to be ideal for allpatients. In particular, generating prescriptions for extending therange of viewing distances without degrading the patient's vision (andsatisfaction with their visual capabilities) can be challenging.

In light of the above, it would be desirable to have improved methods,devices, and systems for treatment of presbyopia. It would be generallydesirable for these improved techniques to be compatible with knownmethods for treating refractive errors of the eye. Ideally, suchimproved eye treatment approaches might be relatively easy to implementwithout significantly increasing the complexity or cost for treatment ofpatients, while increasing the presbyopia treatment efficacy.

BRIEF SUMMARY OF THE INVENTION

The present invention generally provides improved devices, systems, andmethods for treating and/or determining appropriate prescriptions forone or both eyes of a patient. The techniques of the present inventionare particularly well-suited for addressing presbyopia, often incombination with concurrent treatments of other vision defects. In manyembodiments, the techniques of the present invention will intentionallyimpose high-order spherical aberration in one or both of a patient'seyes. This spherical aberration will often comprise a controlled amountof negative spherical aberration extending across a pupil. Conveniently,the desired presbyopia-mitigating quantity of high-order sphericalaberration may be defined by one or more spherical Zernike coefficients.Spherical Zernike coefficients may be readily combined with Zernikecoefficients generated from wavefront aberrometers so as to generate aprescription for a patient which both corrects the undesirableaberrations of the eye and provides at least partial relief frompresbyopia. The prescription can be imposed on the eye using refractivesurgical techniques such as laser eye surgery, using intraocular lensesand other implanted structures, using contact lenses, using temporary orpermanent corneal reshaping techniques, and/or the like.

In a first aspect, the invention provides a method for treatingpresbyopia of a patient having an eye. The method comprises inducing apresbyopia-mitigating quantity of high-order spherical aberration in theeye.

Optionally, the induced spherical aberration may extend across a pupilof the eye. The presbyopia-mitigating quantity may be in a range fromabout 0.05 to about 0.4 microns, often being in a range from about 0.1to about 0.3 microns, and ideally being in a range from about 0.15 toabout 0.25 microns of negative spherical aberration across the pupil.Typically, the spherical aberration will comprise a radially symmetricasphericity. The spherical aberration can be described by at least onesignificant radially symmetric high-order Zernike polynomialcoefficient, and will typically correspond to a plurality ofsignificant, high-order Zernike polynomial coefficients.

For the purpose of refractive correction of an eye, the sphericalaberration may be combined with a plurality of Zernike coefficientscorresponding to the wavefront of that eye. The presbyopia-mitigatingquantity of spherical aberration and refractive defect-correctingprescription may be combined, with the combination induced in the eye byreshaping a cornea, inserting a lens into the eye, positioning a lens infront of the cornea, laser eye surgery, LASEK, LASIK, photorefractivekeratectomy, a contact lens, a scleral lens, an intraocular lens, aphacik intraocular lens, and/or the like.

In some embodiments, refractive aberrations of the eye can be measuredwith a wavefront aberrometer. Wavefront Zernike coefficients of themeasured refractive aberrations may be determined, and a prescriptionmay be defined for the patient by combining the wavefront Zernikecoefficients with at least one high-order Zernike coefficientcorresponding to the presbyopia-mitigating quantity of sphericalaberration.

The image of a point source placed in front of an eye is typically ablurred spot. As the point source moves from a very far distance(optionally defined as mathematical infinity) toward the cornea, theimage may be focused behind the retina. As a result, the image formed onthe retina may be more blurred. In many embodiments it will bepreferable for the treated eye to image a point source as having arelatively intense central spot surrounded by a lower intensity regioninstead of a lower intensity central spot with a higher intensity ring.In this configuration, the image of a larger object formed on the retinacan be sharper as it has more defined edges. Toward that end, thetreated eye can be configured such that a far point source results in afocused spot at the retina and a more intense core and a dimmerperiphery-type image spot forming at distances between the eye lens andthe retina. The treated eye will see objects at a far distance focusedon the retina and objects at near distances form relatively sharp imageson the retina without employing accommodation. Such an object image onthe retina of such an eye can further be focused by utilizing residualaccommodation of the eye.

In many embodiments, the presbyopia-mitigating quantity of sphericalaberration will be identified, and a presbyopia prescription will bedetermined so as to provide the identified quantity of sphericalaberration. The presbyopia-mitigating quantity of spherical aberrationcan be induced by superimposing the determined presbyopia prescriptionon the eye.

In another aspect, the invention provides a method for treatingpresbyopia in a patient having an eye with a pupil. The method comprisesaltering a refraction of the eye so that the altered eye has ahigh-order negative spherical aberration in a range from about 0.1 toabout 0.3 microns across the pupil so that the effect of the presbyopiais mitigated.

In another aspect, the invention provides a method for planning apresbyopia treatment for an eye of a patient having a pupil. A pluralityof Zernike polynomial coefficients correspond to measured aberrations ofthe eye. The method comprises deriving a prescription for the eye bycombining the Zernike polynomial coefficients with at least onehigh-order Zernike polynomial coefficient of a presbyopia-mitigatingnegative spherical aberration.

In yet another aspect, the invention provides a system for treatingpresbyopia. The system comprises a prescription generator module coupledto an output. The prescription generator module defines apresbyopia-mitigating quantity of high-order spherical aberration forthe eye. The output is configured for communication to a lens producingor modifying assembly.

Typically, the prescription generator will have an input coupled to awavefront system. The wavefront system generates a plurality ofrefractive Zernike coefficients corresponding to measured aberrations ofan eye. The lens producing assembly may also comprise a portion of thesystem, with an exemplary lens producing assembly including an ablativelaser for imposing a prescription on the eye by directing a pattern oflaser energy toward a cornea of the eye. The prescription generator maycombine the refractive wavefront correction with a presbyopia-mitigatingwavefront modification. In some embodiments, the prescription generatormay combine the refractive Zernike coefficients with at least onepresbyopia-mitigating Zernike coefficient. The at least onepresbyopia-mitigating Zernike coefficient may include at least onehigh-order Zernike coefficient corresponding to thepresbyopia-mitigating quantity of spherical aberration. This may providethe eye with between about 0.1 and about 0.3 microns of negativespherical aberration across the eye.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a laser ablation system according to an embodiment ofthe present invention.

FIG. 2 schematically illustrates a computer system of the laser systemof FIG. 1.

FIG. 3 illustrates a wavefront measurement system according to anembodiment of the present invention.

FIG. 4 is a flowchart schematically illustrating a method for mitigatingpresbyopia by intentionally imposing high-order spherical aberrationacross a pupil using the laser ablation system of FIG. 1 and thewavefront measurement system of FIG. 3.

FIG. 5 illustrated an optical model of an eye for use in deriving adesired presbyopia-mitigating spherical aberration for use in oneembodiment of the method of FIG. 4.

FIG. 6 graphically illustrates geometrical point spread function (PSF)values for differing spherical aberrations at differing viewingdistances, as calculated with the model of FIG. 5.

FIG. 7 graphically illustrates a comparison of through focus spotdiagrams for eyes having differing spherical aberrations at differingfocal distances.

FIG. 8 graphically illustrates modulation transfer function (MTF) valuesas a function of shift from the focus for differing sphericalaberrations.

FIG. 9 graphically illustrates encircled energy values for differingspherical aberrations and object positions.

FIG. 10 is a table showing exemplary shape parameters of basic andtreated corneas using Zernike polynomial coefficients to define adesired negative asphericity of the cornea.

FIG. 11 is a table showing modulation transfer function (MTF) values at50 cycles/mm for differing object distances.

DETAILED DESCRIPTION OF THE INVENTION

The present invention generally provides devices, systems, and methodsfor treating (and/or planning treatments for) one or both eyes of apatient. The invention provides customized or generalpresbyopia-mitigating shapes, and embodiments of the present inventioncan be readily adapted for use with existing laser systems, wavefrontmeasurement systems, and other optical measurement and refractivecorrection devices, systems, and techniques. While the systems,software, and methods of the present invention are described primarilyin the context of a laser eye surgery system, it should be understoodthe present invention may be adapted for use in alternative eyetreatment devices, procedures, and systems such as spectacle lenses,intraocular lenses, contact lenses, corneal ring implants, collagenouscorneal tissue thermal remodeling, and the like.

Laser ablation procedures can remove the targeted stroma of the corneato change the cornea's contour for varying purposes, such as forcorrecting myopia, hyperopia, astigmatism, and the like. Control overthe distribution of ablation energy across the cornea may be provided bya variety of systems and methods, including the use of ablatable masks,fixed and moveable apertures, controlled scanning systems, eye movementtracking mechanisms, and the like. In known systems, the laser beamoften comprises a series of discrete pulses of laser light energy, withthe total shape and amount of tissue removed being determined by theshape, size, location, and/or number of laser energy pulses impinging onthe cornea. A variety of algorithms may be used to calculate the patternof laser pulses used to reshape the cornea so as to correct a refractiveerror of the eye. Known systems make use of a variety of forms of lasersand/or laser energy to effect the correction, including infrared lasers,ultraviolet lasers, femtosecond lasers, wavelength multipliedsolid-state lasers, and the like. Alternative vision correctiontechniques make use of radial incisions in the cornea, intraocularlenses, removable corneal support structures, and the like.

Referring now to FIG. 1, a laser eye surgery system 10 includes a laser12 that produces a laser beam 14. Laser 12 is optically coupled to laserdelivery optics 16, which directs laser beam 14 to an eye of patient P.A delivery optics support structure (not shown here for clarity) extendsfrom a frame 18 supporting laser 12. A microscope 20 is mounted on thedelivery optics support structure, the microscope often being used toimage a cornea of the eye.

Laser 12 generally comprises an excimer laser, ideally comprising anargon-fluorine laser producing pulses of laser light having a wavelengthof approximately 193 nm. Laser 12 will preferably be designed to providea feedback stabilized fluence at the patient's eye, delivered via laserdelivery optics 16. Embodiments of the present invention may also beuseful with alternative sources of ultraviolet or infrared radiation,particularly those adapted to controllably ablate the corneal tissuewithout causing significant damage to adjacent and/or underlying tissuesof the eye. In some alternate embodiments, the laser beam source mayemploy a solid state laser source having a wavelength between 193 and215 nm as described in U.S. Pat. Nos. 5,520,679 and 5,144,630 to Lin andU.S. Pat. No. 5,742,626 to Mead, the full disclosures of which areincorporated herein by reference. In other embodiments, the laser sourcecomprises an infrared laser as described in U.S. Pat. Nos. 5,782,822 and6,090,102 to Telfair, the full disclosures of which are incorporatedherein by reference. Hence, although an excimer laser is theillustrative source of an ablating beam, other lasers may be used in thepresent invention.

Laser 12 and laser delivery optics 16 will generally direct laser beam14 to the eye of patient P under the direction of a computer system 22.Computer system 22 will often selectively adjust laser beam 14 to exposeportions of the cornea to the pulses of laser energy so as to effect apredetermined sculpting of the cornea and alter the refractivecharacteristics of the eye. In many embodiments, both laser 12 and thelaser delivery optical system 16 will be under control of computersystem 22 to effect the desired laser sculpting process, with thecomputer system effecting (and optionally modifying) the pattern oflaser pulses. The pattern of pulses may be summarized in machinereadable data of tangible media 29 in the form of a treatment table.

Additional components and subsystems may be included with laser system10, as should be understood by those of skill in the art. For example,spatial and/or temporal integrators may be included to control thedistribution of energy within the laser beam, as described in U.S. Pat.No. 5,646,791, the full disclosure of which is incorporated herein byreference. Ablation effluent evacuators/filters, aspirators, and otherancillary components of the laser surgery system are known in the art.Further details of suitable systems for performing a laser ablationprocedure can be found in commonly assigned U.S. Pat. Nos. 4,665,913;4,669,466; 4,732,148; 4,770,172; 4,773,414; 5,207,668; 5,108,388;5,219,343; 5,646,791; and 5,163,934, the complete disclosures of whichare incorporated herein by reference. Suitable systems also includecommercially available refractive laser systems such as thosemanufactured and/or sold by Alcon, Bausch & Lomb, Nidek, WaveLight™,LaserSight™, Schwind, Zeiss Meditec, and the like.

FIG. 2 is a simplified block diagram of an exemplary computer system 22that may be used by the laser surgical system 10 of the presentinvention. Computer system 22 typically includes at least one processor52 which may communicate with a number of peripheral devices via a bussubsystem 54. These peripheral devices may include a storage subsystem56, comprising a memory subsystem 58 and a file storage subsystem 60,user interface input devices 62, user interface output devices 64, and anetwork interface subsystem 66. Network interface subsystem 66 providesan interface to outside networks 68 and/or other devices, such as thewavefront measurement system 30.

User interface input devices 62 may include a keyboard, pointing devicessuch as a mouse, trackball, touch pad, or graphics tablet, a scanner,foot pedals, a joystick, a touchscreen incorporated into the display,audio input devices such as voice recognition systems, microphones, andother types of input devices. User input devices 62 will often be usedto download a computer executable code from a tangible storage media 29embodying any of the methods described herein. In general, use of theterm “input device” is intended to include a variety of conventional andproprietary devices and ways to input information into computer system22.

User interface output devices 64 may include a display subsystem, aprinter, a fax machine, or non-visual displays such as audio outputdevices. The display subsystem may be a cathode ray tube (CRT), aflat-panel device such as a liquid crystal display (LCD), a projectiondevice, or the like. The display subsystem may also provide a non-visualdisplay such as via audio output devices. In general, use of the term“output device” is intended to include a variety of conventional andproprietary devices and ways to output information from computer system22 to a user.

Storage subsystem 56 stores the basic programming and data constructsthat provide the functionality of the various embodiments of the presentinvention. For example, a database and modules implementing thefunctionality of the methods of the present invention, as describedherein, may be stored in storage subsystem 56. These software modulesare generally executed by processor 52. In a distributed environment,the software modules may be stored on a plurality of computer systemsand executed by processors of the plurality of computer systems. Storagesubsystem 56 typically comprises memory subsystem 58 and file storagesubsystem 60.

Memory subsystem 58 typically includes a number of memories including amain random access memory (RAM) 70 for storage of instructions and dataduring program execution and a read only memory (ROM) 72 in which fixedinstructions are stored. File storage subsystem 60 provides persistent(non-volatile) storage for program and data files, and may includetangible storage media 29 (FIG. 1) which may optionally embody wavefrontsensor data, wavefront gradients, a wavefront elevation map, a treatmentmap, and/or an ablation table. File storage subsystem 60 may include ahard disk drive, a floppy disk drive along with associated removablemedia, a Compact Digital Read Only Memory (CD-ROM) drive, an opticaldrive, DVD, CD-R, CD-RW, solid-state removable memory, and/or otherremovable media cartridges or disks. One or more of the drives may belocated at remote locations on other connected computers at other sitescoupled to computer system 22. The modules implementing thefunctionality of the present invention may be stored by file storagesubsystem 60.

Bus subsystem 54 provides a mechanism for letting the various componentsand subsystems of computer system 22 communicate with each other asintended. The various subsystems and components of computer system 22need not be at the same physical location but may be distributed atvarious locations within a distributed network. Although bus subsystem54 is shown schematically as a single bus, alternate embodiments of thebus subsystem may utilize multiple busses.

Computer system 22 itself can be of varying types including a personalcomputer, a portable computer, a workstation, a computer terminal, anetwork computer, a control system in a wavefront measurement system orlaser surgical system, a mainframe, or any other data processing system.Due to the ever-changing nature of computers and networks, thedescription of computer system 22 depicted in FIG. 2 represents only anexample for purposes of illustrating one embodiment of the presentinvention. Many other configurations of computer system 22 are possiblehaving more or less components than the computer system depicted in FIG.2.

Referring now to FIG. 3, one embodiment of a wavefront measurementsystem 30 is schematically illustrated in simplified form. In verygeneral terms, wavefront measurement system 30 is configured to senselocal slopes of a wavefront exiting the patient's eye. Devices based onthe Hartmann-Shack principle generally include a lenslet array to samplethe slopes across the pupil of the eye. Thereafter, the local slopes areanalyzed so as to reconstruct the wavefront surface or map, often usingZernike polynomial expansion methods.

More specifically, one wavefront measurement system 30 includes a lightsource 32, such as a laser, which projects a source image throughrefractive tissues 34 of eye E so as to form an image 44 upon a surfaceof retina R. The image from retina R is transmitted by the refractivesystem of the eye (e.g., refractive tissues 34) and imaged onto awavefront sensor 36 by system optics 37. The wavefront sensor 36communicates signals to a computer system 22′ for measurement of theoptical errors in the optical tissues 34 and/or determination of anoptical tissue ablation treatment program. Computer 22′ may include thesame or similar hardware as the computer system 22 illustrated in FIGS.1 and 2. Computer system 22′ may be in communication with computersystem 22 that directs the laser surgery system 10, or some or all ofthe computer system components of the wavefront measurement system 30and laser surgery system 10 may be combined or separate. If desired,data from wavefront sensor 36 may be transmitted to a laser computersystem 22 via tangible media 29, via an I/O port, via a networkingconnection 66 such as an intranet or the Internet, or the like.

Wavefront sensor 36 generally comprises a lenslet array 38 and an imagesensor 40. The reflected light from retina R is transmitted throughoptical tissues 34 and imaged onto a surface of image sensor 40 and theeye pupil P is similarly imaged onto a surface of lenslet array 38. Thelenslet array separates the transmitted light beam into an array ofbeamlets 42, and (in combination with other optical components of thesystem) images the separated beamlets on the surface of sensor 40.Sensor 40 typically comprises a charged couple device or “CCD,” andsenses the characteristics of these individual beamlets, which can beused to determine the characteristics of an associated region of opticaltissues 34. In particular, where image 44 comprises a point or smallspot of light, a location of the transmitted spot as imaged by a beamletcan directly indicate a local gradient of the associated region ofoptical tissue.

Eye E generally defines an anterior orientation ANT and a posteriororientation POS. Light source 32 generally sends light in a posteriororientation through optical tissues 34 onto retina R as indicated inFIG. 3. Optical tissues 34 again transmits light reflected from theretina anteriorly toward wavefront sensor 36. Image 44 actually formedon retina R may be distorted by any imperfections in the eye's opticalsystem when the image source is originally transmitted by opticaltissues 34. Optionally, image projection optics 46 may be configured oradapted to decrease any distortion of image 44.

In some embodiments, projection optics 46 may decrease lower orderoptical errors by compensating for spherical and/or cylindrical errorsof optical tissues 34. Higher order optical errors of the opticaltissues may also be compensated through the use of an adaptive opticssystem, such as a deformable mirror. Use of a light source 32 selectedto define a point or small spot at image 44 upon retina R may facilitatethe analysis of the data provided by wavefront sensor 36. Regardless ofthe particular light source structure, it will be generally bebeneficial to have a well-defined and accurately formed image 44 onretina R.

The wavefront data may be stored in a computer readable medium 29 or amemory of the wavefront sensor system 30 in two separate arrayscontaining the x and y wavefront gradient values obtained from imagespot analysis of the Hartmann-Shack sensor images, plus the x and ypupil center offsets from the nominal center of the Hartmann-Shacklenslet array, as measured by the pupil camera 51 (FIG. 3) image. Suchinformation may include all the available information on the wavefronterror of the eye and is typically sufficient to reconstruct thewavefront or a desired portion of it. In such embodiments, there may beno need to reprocess the Hartmann-Shack image more than once, and thedata space required to store the gradient array is not large. Forexample, to accommodate an image of a pupil with an 8 mm diameter, anarray of a 20×20 size (i.e., 400 elements) is often sufficient. As canbe appreciated, in other embodiments, the wavefront data may be storedin a memory of the wavefront sensor system in a single array or multiplearrays.

While embodiments of the invention will generally be described withreference to sensing of an image 44, it should be understood that aseries of wavefront sensor data readings may be taken. For example, atime series of wavefront data readings may help to provide a moreaccurate overall determination of the ocular tissue aberrations. As theocular tissues can vary in shape over a brief period of time, aplurality of temporally separated wavefront sensor measurements canavoid relying on a single snapshot of the optical characteristics as thebasis for a refractive correcting procedure. Still further alternativesare also available, including taking wavefront sensor data of the eyewith the eye in differing configurations, positions, and/ororientations. For example, a patient will often help maintain alignmentof the eye with wavefront measurement system 30 by focusing on afixation target, as described in U.S. Pat. No. 6,004,313, the fulldisclosure of which is incorporated herein by reference. By varying aposition of the fixation target as described in that reference, opticalcharacteristics of the eye may be determined while the eye accommodatesor adapts to image a field of view at a varying distance and/or angles.

Referring now to FIG. 4, a method for treating presbyopia will generallyinclude measurement of a wavefront of an eye using a wavefront sensor,such as that schematically illustrated in FIG. 3. In many embodiments,Zernike coefficients of the wavefront will be determined 106. Thewavefront and Zernike coefficients can be used to directly determine arefractive prescription so as to correct optical aberrations of the eye.Known wavefront-based optical corrections often seek to correct orcompensate for all optical aberrations of the eye so that the eye is,after treatment, emmetropic.

In exemplary method 102, rather than developing a prescription so as toprovide an emmetropic eye, a presbyopia-mitigating high-order sphericalaberration is determined 108. This desired spherical aberration,together with the Zernike coefficients from the wavefront, are used todetermine a prescription 110, with the prescription generally leavingthe treated eye with the desired spherical aberration while correctingother high-order and standard refractive errors. The prescription isthen imposed on the eye 112, optionally using a laser eye surgery systemsuch as that illustrated in FIG. 1.

Wavefront measurements may be taken using a variety of commerciallyavailable systems, with an exemplary wavefront measurement systemcomprising a VISX WaveScan™ system, available from VISX, Incorporated ofSanta Clara, Calif. Alternative wavefront measurement systems includethose described in, for example, U.S. Pat. No. 6,271,915. Still furtheralternative wavefront measurement systems may be employed, with thepreferred systems measuring the wavefront using light which has beentransmitted through the refractive tissues of the eye from a retina, asdescribed above.

While exemplary presbyopia-mitigating method 102 determines Zernikecoefficients of the wavefront 106, alternative methods may employ any ofa variety of alternative mathematical frameworks so as to define thewavefront. For example, direct wavefront-based corneal ablationtreatment prescriptions may be derived using methods and systems such asthose described in U.S. patent application Ser. No. 10/006,992, the fulldisclosure of which is incorporated herein by reference. Wavefrontreconstruction using Fournier transformations and direct integration mayalso be employed, including the techniques described in U.S. patentapplication Ser. No. 10/872,107, the full disclosure of which is alsoincorporated herein by reference. Regardless, the wavefrontreconstruction will generally correspond to at least some amount ofirregular aberration of the eye. By basing a prescription at least inpart on such irregular aberrations, the treatments described herein mayprovide visual acuities of at least 20/20 or better, in some casesproviding visual acuities of better than 20/20, often along withpresbyopia-mitigation.

A number of approaches may be employed to determine a desiredpresbyopia-mitigating high-order spherical aberration 108. As usedherein, high-order spherical aberration encompasses sphericalaberrations other than standard myopia and hyperopia. Desired sphericalaberration may be determined based on empirical data, simple or complexmodels of the refractive tissues, and the like. When the wavefrontreconstruction comprises Zernike coefficients, the desiredpresbyopia-mitigating spherical aberration may conveniently be modeledas radially symmetric Zernike polynomial expansion coefficients, such asterms Z(2, 0), Z(4, 0), Z(6, 0), and the like. In other embodiments,different mathematical formulations of the desired spherical aberrationmay be employed.

When the wavefront reconstruction 106 and presbyopia-mitigatingspherical aberration 108 have been defined using Zernike polynomials,the combined prescription 110 may be directly calculated bysuperimposing the appropriate asphericity on the eye while otherwisecorrecting the wavefront error. This can be as easy as adding orsubtracting the appropriate polynomial terms to the measured wavefront.Where other reconstruction techniques are employed, or where the desiredpresbyopia-mitigating spherical aberration is defined in mathematicalterms which differ from that of the wavefront reconstruction, morecomplex analytical approaches for determining the combined prescriptionmay be employed.

Once the desired prescription has been determined 110, that prescriptionmay be imposed on the eye 112 using any of a wide variety of alternativerefraction altering approaches. For example, custom contact lenses maybe laser ablated or otherwise formed, intraocular or phacik lenses maybe shaped by lasers or other sculpting techniques, selective cornealcollagen contraction using laser or other heating methodologies may beemployed, or the like. Regardless, in many embodiments, the desiredspherical aberration will extend across a pupil of the patient after thetreatment is complete, and often after any associated healing takesplace.

Addressing how to determine a desired high-order spherical aberration108 so as to mitigate presbyopia, the human eye generally has multiplerefractive elements including a cornea, crystalline lens, and vitreousfluid. An object is seen in focus when a sharp image of that object isformed on the retina R, as schematically illustrated in FIG. 5. Therange of distances throughout which an object will appear in focusdepends at least in part on accommodation of the crystalline lens.Assuming the accommodation of the lens is small or negligible (which mayhappen as a person ages) the viewed object will appear blurry as itmoves away from a best viewing distance. Changes in imagecharacteristics with changes in viewing distance may also be related to(and may correspond to) changes in the image characteristics withchanges in an image focal plane or focal distance anterior of and/orposterior to the retina. The rate at which the object becomes blurrydepends on the optical properties of the eye and the pupil diameter. Theblurring of the image with changes in focal distance may be reduced byapplying an appropriate optical correction to the eye. The desiredcorrections will generally be described herein as being applied to thecornea using laser ablation, although other refractive treatmentmodalities may alter refraction anterior to the cornea (such as using acontact lens or scleral lens) or posterior of the cornea (intraocularlenses, or the like).

Spherical aberrations are radially symmetric aberrations of the opticalsystem, and may cause light passing through the different parts of thepupil to focus at different distances from the cornea. Consequently, theimage of a point source of light may become a blurred spot, or the like.A relative position of paraxial and peripheral images (as imaged withina central region of the pupil and a peripheral region of the pupil,respectively) along the optical axis may determine a sign of thespherical aberration. When the paraxial focal length of the opticalsystem is shorter than the peripheral focal distance, the sphericalaberration has a negative sign, and when the paraxial focal length ofthe optical system is longer than the peripheral focal distance, thespherical aberration has a positive sign.

Human eyes typically have a small amount of spherical aberration, aswill generally be identified in wavefront measurements of the eye 104.Post-surgical eyes and/or pathological eyes may have significantquantities of spherical aberration. Retinal image quality may depend onboth the magnitude or quantity of spherical aberration, and on the signof spherical aberration. As described hereinbelow, negative sphericalaberration may provide better depth of focus, and may therefore providemore desirable presbyopia mitigation capabilities.

Referring now to FIG. 5, a simplified analytical model 120 of an eye canbe useful in determining presbyopia-mitigating high-order sphericalaberration. The model illustrated in FIG. 5 comprises a ZEMAX™ opticaldesign software model developed using software commercially availablefrom ZEMAX Development Corporation of San Diego, Calif. Model Eye 120includes an anterior cornea 122, which may be modeled as an evenaspheric surface with a single conic constant. In other words, modelcornea 122 comprises an ellipsoid with even order radial terms added tomake it an aspheric surface. The radial terms used may comprise up to8^(th) order for the anterior cornea. Central curvature, conic constant,and coefficients of the radial aspheric terms may be variables in model120, so that the spherical aberration of the eye can be varied byadjusting these parameters.

Using the eye model 120, encircled energy, modulation transfer function(MTF) at a chosen frequency, and geometrical point spread function(PSF), can be computed to estimate image quality for different sphericalaberrations and object distances. Polychromatic calculations can beperformed using a plurality of wavelengths of light, often using threeor more wavelengths of light, such as 0.45 microns, 0.55 microns, and0.65 microns light. Weighting factors of 0.04, 1, and 0.35 may beapplied to the wavelengths specified above, respectively. While pupilsize may be varied in some analyses, at least some of the calculationsdescribed below were done with a single 6 mm entrance pupil size, withthe imaged object being positioned on the optical axis of the model eye.

Referring now to FIG. 6, geometrical pointspread functions werecalculated with the model eye of FIG. 5 at differing sphericalaberrations SA. An object, and specifically a light point source, wasmodeled at an infinite distance (V=0 D) and at 2 meters (V=0.5 D) fromthe eye in which V is the vergence. FIG. 6 graphically represents across section of the geometric point spread function for the model eyewith a spherical aberration SA of about zero, of −0.2 microns, and of+0.21 microns. In the graph of FIG. 6, the horizontal or x axisrepresents the position in microns on the retina, with the distancesmeasured from the optical axis of the eye. One micron length on theretina subtends to approximately 0.2 arc minutes of angle at the centerof the corneal lens.

The geometric point spread function (PSF) peak is highest for the casein which little or no spherical aberration is present and the object isat an infinite distance. However, the pointspread function of this modeleye spreads rapidly as the object comes closer to the eye, with thesubstantially zero spherical aberration model at a 0.5 D vergence havinga much lower peak height. In contrast, the change in peak height withchanges in vergence is significantly smaller for the model eye havingnegative spherical aberration (SA −0.2, VOD/0.5 D). Along with thereduction in peak height change, the model eye with negative sphericalaberration has a point spread function which stays more localized as theobject moves from an infinite distance to 2 meters (on other words, asvergence V changes from 0 to 0.5 D).

Referring now to FIG. 7, an array of through focus spot diagrams 130graphically illustrates images of a point source when the eye hasvarying amounts of spherical aberration and the image plane is atvarying distances from the cornea. Through focus spot diagrams areprovided for an eye having little or no spherical aberration, SA=0; aneye having negative spherical aberration, SA=−0.2; and an eye havingpositive spherical aberration SA=+0.2. The numbers appearing along thebottom of the array 130 indicate a distance along the optical axis atwhich the associated through focus spot diagrams are analyzed, with the“0” position being at the best focus point, typically located at theretina R (as indicated by the best focal plane for infinity 132).Positive numbers to the right side of the array indicate distancesfarther from the cornea as measured from the best focus point, while thenegative numbers on the left side of the array represent positionscloser to the corneal lens of the eye model. As a point source movesfrom infinity closer to the eye, the image at the retina (for an eyewithout accommodation) will change in the direction of arrow 134. Thus,the image of the point source formed at the retina would be a spotdiagram more to the left side of the central spot. The measurementsindicated are in microns.

As indicated along the top of the array, the best focus spot size issmallest for the SA=0 case. Note that for negative spherical aberration,the spot diagrams include a relatively high intensity central region onthe left side of the array (at imaging distances closer to the corneathan the best paraxial focus point), while this same model has spotdiagrams which spread out more evenly on the right side of the array (atgreater distances from the best paraxial focus point). Thischaracteristic is reversed in the case in which spherical aberration ispositive, with the spot having an intense central region on the rightside of the array (at greater distances), while the positive sphericalaberration results in even spreading of the spot at nearer focaldistances toward the left side of the array.

Having a relatively intense central region with a dim peripheral tailmay create a sharper image as compared to a spot diagram having an evendistribution or a higher intensity at the periphery of the spot.Additionally, having an intense central spot at focal distances in frontof the retina (closer to the cornea and/or along the left side of thearray of FIG. 7) may be useful. More specifically, when an object movescloser to such an eye, the image on the retina is sharper. Additionally,the eye may be able to accommodate (using any residual accommodation) soas to focus an even sharper image onto the retina. The image of closeobjects is less sharp if a point source generates an intense centralspot which is located posteriorly of the retina. Hence, the negativespherical aberration through focus spot diagrams across the middle rowof array 130 appear to provide benefits by providing a long depth offocus, as any accommodative abilities remaining in the eye can assistthe patient in bringing the intense central regions into focus.Furthermore, the change in retinal spot size (with varying distances)with such negative spherical aberration may be less than for thepositive spherical aberration case, and/or than correspondingsubstantial changes in spot size of the zero spherical aberration case.

Referring now to FIG. 8, the modulation transfer function (MTF) at 50cycles/mm is shown as a function of distance from the focus. As was thecase with the through focus spot diagrams of FIG. 7, the modulationtransfer function may be highest at about the focus for the zerospherical aberration case. However, for distances which are less thanthe focus (and again closer to the cornea, here again having negativevalues along the x axis), the MTF for the model eye having a negativespherical aberration increases and actually exceeds the modulationtransfer function value for the zero spherical aberration case when theshift from best focus is greater than 50 microns.

Assuming an eye has no accommodation (effectively having a fixed lens),if an object is placed at infinity and moves closer to the eye, theimage location or focus will move away from the cornea and/or away fromthe retina. This may imply that a position of the retina may be closerto the cornea than the best image location. In other words, the retinamay be located at a negative shift distance from the focus as the objectis placed closer to the eye. In such situations, the MTF of the negativespherical aberration eye may be better than the substantially zerospherical aberration eye or the positive spherical aberration eye, asthe modulation transfer function changes more slowly and stays at amoderate (and often acceptable) level when objects move closer to theeye.

Referring now to FIG. 9, encircled energy for different sphericalaberrations (SA again being specified in microns) and object positions(again being specified in vergence with V=0 being an object at infinityand V+0.5 D being an object at 2 meters from the eye) are shown. Thisencircled energy graph indicates that an appropriate quality of negativespherical aberration may provide benefits similar to those describedabove regarding the PSF and the MTF. More specifically, the graphicaldata of FIG. 9 shows plots of geometric encircled energy calculated forpolychromatic point sources placed on the optical axis at the indicatedvergence distances. For comparison, a graph of a diffraction limitedoptical system is also shown. Per FIG. 9, as an object is moved frominfinity to 2 meters, the radius to encompass a given fraction of thetotal energy increases. The change in the radius is smaller when thespherical aberration is negative, and is greater when the sphericalaberration is positive.

The above indicates that an eye having an appropriate negative sphericalaberration can provide a greater depth of focus. Hence, such negativespherical aberration may be beneficial to the eye to achieve mitigationof presbyopia and provide better vision despite changes in viewingdistances. The above simulation data on pointspread functions,modulation transfer functions, and encircled energy support the abilityof negative spherical aberration to alleviate the limited viewing depthof presbyopia. Each of these image quality characteristics showedsmaller variation as an object position is shifted from infinity tosomewhere closer to the eye when the eye has an appropriate negativespherical aberration, as opposed to a positive spherical aberration orsubstantially no spherical aberration. Any remaining residualaccommodation of the eye may further enhance image quality factors foran eye having negative spherical aberration.

The Table illustrated in FIG. 10 shows an example of shape parameters ofan initial or basic cornea and a corrected or treated cornea (both asmodeled using an optical model similar to that of FIG. 5). Once again,the negative spherical aberration identified in FIG. 10 is assumed to beintroduced through negative asphericity of the cornea, such as might beimposed by laser eye surgery, a contact lens, or the like. Thecoefficients shown in the table of FIG. 10 are standard Zernikepolynomial coefficients, and the optimized coefficient values have beenspecified so as to enhance the benefit of the negative sphericalaberration in the optical matrix described above. The amount of negativespherical aberration was changed to derive a shape that provideddesirable characteristics on the optical matrix described above. The MTFand PSF, as described above, were utilized for this optimization.

Referring now to FIG. 11, a result of the optimization shows values ofmodulation transfer function at 50 cycles/mm for different objectdistances. The modulation transfer function was calculatedgeometrically, and the values are for polychromatic light with a 4 mmpupil size.

The values given in FIG. 11 indicate that a drop in the modulationtransfer function as an object is moved away from the best focuslocation is much slower for the optimized cornea than for a standardcornea. The slower change in modulation transfer function implies agreater depth of field for the eye treated with the optimized shape ofFIG. 10. The effect of 1.0 D reading glasses are also shown.

While the exemplary embodiments have been described in some detail, byway of example and for clarity of understanding, those of skill in theart will recognize that a variety of modification, adaptations, andchanges may be employed. Hence, the scope of the present inventionshould be limited solely by the appending claims.

What is claimed is:
 1. A system for manufacturing an intraocular lensthat extends a range of viewing distances without degrading a patient'svision, the system comprising: a sensor that measures a plurality ofrefractive Zernike coefficients corresponding to aberrations of an eye,wherein the eye includes a pupil, a cornea and a retina; a communicationinterface that is communicatively coupled to a lens producing assembly;and a processor communicatively coupled to the sensor and thecommunication interface, wherein the processor: receives, from thesensor, the plurality of refractive Zernike coefficients, defines aprescription of the intraocular lens by combining the plurality ofrefractive Zernike coefficients with at least one high-order sphericalaberration Zernike coefficient, wherein the prescription results in aneye that forms an image of a point source disposed at a viewing distancefrom the eye at a plane between the cornea and the retina, and the imagehas a central area with a central intensity surrounded by a peripheralarea with a peripheral intensity, the central intensity being higherthan the peripheral intensity, and controls the lens producing assemblyto manufacture the intraocular lens according to the prescription,wherein a surgical implantation of the intraocular lens in the eyeresults in an altered eye that has a presbyopia-mitigating quantity ofhigh-order negative spherical aberration.
 2. The system of claim 1,wherein the sensor is a wavefront sensing system.
 3. The system of claim1, wherein the presbyopia-mitigating quantity of high-order negativespherical aberration is in a range from 0.05 to 0.4 microns of negativespherical aberration across the pupil.
 4. The system of claim 3, whereinthe presbyopia-mitigating quantity of high-order negative sphericalaberration is in a range from 0.1 to 0.3 microns of negative sphericalaberration across the pupil.
 5. The system of claim 4, wherein thepresbyopia-mitigating quantity of high-order negative sphericalaberration is in a range from 0.15 to 0.25 microns of negative sphericalaberration across the pupil.
 6. The system of claim 1, wherein the atleast one high-order spherical aberration Zernike coefficient comprisesa plurality of high-order spherical aberration Zernike coefficients. 7.A system for manufacturing an intraocular lens that extends a range ofviewing distances without degrading a patient's vision, the systemcomprising: a lens-producing assembly; and a processor communicativelycoupled to the lens producing assembly, wherein the processor: receivesa plurality of refractive Zernike coefficients corresponding toaberrations of an eye, wherein the eye includes a pupil, a cornea and aretina; defines a prescription of the intraocular lens by combining theplurality of refractive Zernike coefficients with at least onehigh-order spherical aberration Zernike coefficient, wherein theprescription results in an eye that forms an image of a point sourcedisposed at a viewing distance from the eye at a plane between thecornea and the retina, and the image has a central area with a centralintensity surrounded by a peripheral area with a peripheral intensity,the central intensity being higher than the peripheral intensity, andcontrols the lens-producing assembly to manufacture the intraocular lensaccording to the prescription, wherein a surgical implantation of theintraocular lens in the eye results in an altered eye that has apresbyopia-mitigating quantity of high-order negative sphericalaberration.
 8. The system of claim 7, wherein the plurality ofrefractive Zernike coefficients corresponding to the aberrations of theeye are received from a wavefront sensing system.
 9. The system of claim7, wherein the presbyopia-mitigating quantity of high-order negativespherical aberration is in a range from 0.05 to 0.4 microns of negativespherical aberration across the pupil.
 10. The system of claim 9,wherein the presbyopia-mitigating quantity of high-order negativespherical aberration is in a range from 0.1 to 0.3 microns of negativespherical aberration across the pupil.
 11. The system of claim 10,wherein the presbyopia-mitigating quantity of high-order negativespherical aberration is in a range from 0.15 to 0.25 microns of negativespherical aberration across the pupil.
 12. The system of claim 7,wherein the at least one high-order spherical aberration Zernikecoefficient comprises a plurality of high-order spherical aberrationZernike coefficients.